On transitive polynomials modulo integers

Mohammad Javaheri and Gili Rusak
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 2, Pages 23—35
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Authors and affiliations

Mohammad Javaheri
School of Science, Siena College
515 Loudon Road, Loudonville, NY 12110, USA

Gili Rusak
School of Engineering, Stanford University
353 Serra Mall, Stanford, CA 94305, USA


A polynomial P(x) with integer coefficients is said to be transitive modulo m, if for every x, y ∈ ℤ there exists k ≥ 0 such that Pk(x) = y (mod m). In this paper, we construct new examples of transitive polynomials modulo prime powers and partially describe cubic and quartic transitive polynomials. We also study the orbit structure of affine maps modulo prime powers.


  • Transitive polynomials
  • Permutation polynomials

AMS Classification

  • 11T06



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Cite this paper

Javaheri, M., & Rusak, G. (2016). On transitive polynomials modulo integers. Notes on Number Theory and Discrete Mathematics, 22(2), 23-35.

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